3[5-3b+t]-3=5[3(5t-4)+8]-45

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Solution for 3[5-3b+t]-3=5[3(5t-4)+8]-45 equation: 


Simplifying
3[5 + -3b + t] + -3 = 5[3(5t + -4) + 8] + -45
[5 * 3 + -3b * 3 + t * 3] + -3 = 5[3(5t + -4) + 8] + -45
[15 + -9b + 3t] + -3 = 5[3(5t + -4) + 8] + -45

Reorder the terms:
15 + -3 + -9b + 3t = 5[3(5t + -4) + 8] + -45

Combine like terms: 15 + -3 = 12
12 + -9b + 3t = 5[3(5t + -4) + 8] + -45

Reorder the terms:
12 + -9b + 3t = 5[3(-4 + 5t) + 8] + -45
12 + -9b + 3t = 5[(-4 * 3 + 5t * 3) + 8] + -45
12 + -9b + 3t = 5[(-12 + 15t) + 8] + -45

Reorder the terms:
12 + -9b + 3t = 5[-12 + 8 + 15t] + -45

Combine like terms: -12 + 8 = -4
12 + -9b + 3t = 5[-4 + 15t] + -45
12 + -9b + 3t = [-4 * 5 + 15t * 5] + -45
12 + -9b + 3t = [-20 + 75t] + -45

Reorder the terms:
12 + -9b + 3t = -20 + -45 + 75t

Combine like terms: -20 + -45 = -65
12 + -9b + 3t = -65 + 75t

Solving
12 + -9b + 3t = -65 + 75t

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -9b + -12 + 3t = -65 + -12 + 75t

Reorder the terms:
12 + -12 + -9b + 3t = -65 + -12 + 75t

Combine like terms: 12 + -12 = 0
0 + -9b + 3t = -65 + -12 + 75t
-9b + 3t = -65 + -12 + 75t

Combine like terms: -65 + -12 = -77
-9b + 3t = -77 + 75t

Add '-3t' to each side of the equation.
-9b + 3t + -3t = -77 + 75t + -3t

Combine like terms: 3t + -3t = 0
-9b + 0 = -77 + 75t + -3t
-9b = -77 + 75t + -3t

Combine like terms: 75t + -3t = 72t
-9b = -77 + 72t

Divide each side by '-9'.
b = 8.555555556 + -8t

Simplifying
b = 8.555555556 + -8t

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